Certainly! Let's solve the given expression step by step:
The expression is:
[tex]\[ 4 \div (-6 - 4 + 3) + \left[ 15 \div (-7 + 2) - 9 \right] \div 6 \][/tex]
### Step 1: Simplify the first part [tex]\(4 \div (-6 - 4 + 3)\)[/tex]
1. Simplify inside the parentheses:
[tex]\[ -6 - 4 + 3 = -7 \][/tex]
2. Substitute back into the division:
[tex]\[ 4 \div (-7) = -\frac{4}{7} \approx -0.5714285714285714 \][/tex]
### Step 2: Simplify the second part [tex]\( \left[ 15 \div (-7 + 2) - 9 \right] \div 6 \)[/tex]
1. Simplify inside the parentheses:
[tex]\[ -7 + 2 = -5 \][/tex]
2. Substitute back into the division:
[tex]\[ 15 \div (-5) = -3 \][/tex]
3. Now, subtract 9 from the result:
[tex]\[ -3 - 9 = -12 \][/tex]
4. Divide the result by 6:
[tex]\[ -12 \div 6 = -2 \][/tex]
### Step 3: Combine the results
Now we add the results of the first part and the second part:
[tex]\[ -0.5714285714285714 + (-2) = -2.571428571428571 \][/tex]
### Final Result
The value of the given expression is:
[tex]\[ 4 \div (-6 - 4 + 3) + \left[ 15 \div (-7 + 2) - 9 \right] \div 6 = -2.571428571428571 \][/tex]
